Probably the most efficient and useful shortcut I ever learned in my (fortunately) short micro-math career. How it never occurred to my prof to teach this absolutely basic thing is beyond me. Thank you!
This is quite possibly the most god breathed video EVER. Was literally bawling my eyes out today in the library trying to finish my homework. thank you so much
Well, there are two types of videos- numerical and analytical. Usually as you move toward higher and higher levels of analysis, you see fewer and fewer numbers (and even fewer equations!) as you try to generalize to more and more general situations. I have both kinds of videos- most of them with numbers! Check out my video list in the right hand column on www.burkeyacademy.com/home/microeconomics for a large selection of numerical goodness!
Absolutely. As long as the production function is a Cobb-Douglas type, of the form Q=A*L^a *K^b, the MRS is the same as the MRTS. If there is a multiplier (like the A), it cancels out of the MRTS equation since it will be on top and bottom. It is the same mathematics as for MRS.
No, I tried to make it clear that this shortcut only works for Cobb-Douglas- watch the video to see why. Every other kind of function is going to have very different looking derivatives, and MU, and thus MRS. However, there are some different ways (monotonic transformations) to transform a Cobb-Douglas that still represent Cobb-Douglas preferences. One example is to take the log of U: U=a*ln(x) + b*ln(y): The MRS will still be ay/bx.
Okay thanks a bunch! So for example the question is Q=f(L,K)=5KL^(1/4) I can use the rules in the video and assume that the MRTS = 1/4K / L or K/4L, and I can disregard the 5 because it cancels out?
I'm getting a different answer for the first example. I get MUx= 0.2y^0.4 x^-0.8 and MUy=0.4x^0.2 y^-0.6 and then MRS = 0.5yx^-1.Why is that different than the shortcut/easy way?
Thanks for the video. Can I ask a simple question? The last example you wanted us to solve is U=x^0.7*y^0.1, right? Isn't a+b always equal to 1? On my textbook, Cobb-Douglas production function is: QO=A(K^aL^(1-a)) 109=A(30^.3*70^.7) A equals to 2, right? Can you please explain to me what "A=2" means here? Why do we need to calculate this? Thanks again
Great questions. Question 1: a+b does not have to be =1. However, for Cobb-Douglas utility functions you CAN force a+b to be = 1, and it can still represent all possibly Cobb-Douglas Utility functions. Let me make a video about that- I have been meaning to, and can explain it very well that way very quickly. I am going to do my best to make a video about it in the next few hours. Please remind me if you don't see one soon, OK? Question 2: Same thing... let me make a short video response to this to try to explain WHY someone might force you to do this. Typing a response would bee hard and confusing! I'll go get a cup of coffee and see if I can get started!
So monotinicity transforms the cobb-douglas function to: U= x1^a . x2^1-a So wouldnt it be solved as: (du/dx1)/(du/dx2) ,therefore; -a/(1-a) . x2/x1 ? Is this as simple as it gets?
in my text book has MRS= -U1/U2. with the negative in front. whats the difference? I think it should be negative since the indifference curve is downward sloping.
Yes, technically the slope is negative if both x and y are goods, and the slope of the budget line is negative as well. So, when solving MRS=Px/Py, I just cancel the negatives. Also, while the slope is negative, the MRS is a quantity that can be thought of as an absolute value: How many y you are willing to trade for 1 more x.
Thanks for the help. but does this work for MRTS when there are integers in front of X and Y, for example, q=10F^1/3 * K^2/3 ? Doesn't seem to be working for me, unless I've missed something silly.
Yes it does! The integers cancel out, since when you take the partial derivatives the 10 will appear in the numerator and denominator. One thing to be careful of is where you put your Pk and Pf-- that may be messing you up.
No, this is the first time I have heard of that book. Solving all of the exercises for one certain book is not something that would be interesting to do. But, if there is a TYPE of problem you would like help understanding, let me know.!
Most economists, and most textbooks call MRS the absolute value (and similarly with the marginal rate of transformation). Similar to the price elasticity of demand, we are not interested in the sign, but the magnitude. Yes, there are a few sources that insist on the (-) sign, but it isn't important as long as you are consistent.
Finally a video where the math and calculus is explained!!! You have no clue what this means to so many students!!
Thanks! I am glad it helped!
Probably the most efficient and useful shortcut I ever learned in my (fortunately) short micro-math career. How it never occurred to my prof to teach this absolutely basic thing is beyond me. Thank you!
Why do professors make it so complicated in Universities! Thank you man got it! :)
I assume we are from the same uni hhhh
I think its is the same in many universities. They make simple things complicated
i love you for this video. my professor had my head burning with his lecture. this is so simple. thank you!!!
This is quite possibly the most god breathed video EVER. Was literally bawling my eyes out today in the library trying to finish my homework. thank you so much
Oh my! Glad you are all better now!
You have no idea how much this helps! Thank you so so much. Uni really over complicated it for no reason.
THANK YOU SO SO MUCH, seriously you have no idea how much you saved me and my grades
why on Earth does literally nobody use numbers? I don't understand without a practical example!
Well, there are two types of videos- numerical and analytical. Usually as you move toward higher and higher levels of analysis, you see fewer and fewer numbers (and even fewer equations!) as you try to generalize to more and more general situations. I have both kinds of videos- most of them with numbers! Check out my video list in the right hand column on www.burkeyacademy.com/home/microeconomics for a large selection of numerical goodness!
Ikr ive been looking for 30 minutes all useless videos
Absolutely. As long as the production function is a Cobb-Douglas type, of the form Q=A*L^a *K^b, the MRS is the same as the MRTS. If there is a multiplier (like the A), it cancels out of the MRTS equation since it will be on top and bottom. It is the same mathematics as for MRS.
Your page is underrated. Thank you so much!!!
please keep doing what you do
This was incredibly well explained and really clarified many questions I had. Thank you so much!
you wonderful human you.
bless.
OMG! You have saved me sir. I just couldn't understand it until now. Thank you!
Thanks!!! Superior tutorial, finally I understood how I should solve my homework. Million of thanks for saving my day!!!
This video is an absolute lifesaver, thank you!!!
finally - able to understand...MRS - COBB DOUGLAS AND MU
thank you so much for this video!!!! It's really made my life easier.
Thank you so much. very well and simply explained
Thanks, Profesor, you really help me to understand that step of content.
exactly what i need.. an explanation for newbies.. keep it simple dude.. :)
I wish you to be happy all the time as you made me so
You’re the goat for goin over the calculus 🫶🏾
wow!!! well explained and so easy to understand!!!
Thank you SO MUCH for this video!
Thank you very much) wow, now i understand this topic!)
nice tutorial very easy to understand compared to my lecurer.......please upload more content.........Brian G. Nairobi,Kenya.
Thx dude 🎉
thanx so much for this video......it was simple to understand cobb douglas
Thank You Sir 😊🙏🏻
.2/.4=0.5. Another way to write this is 1/2. Make sense?
God bless you!!
helpful video
Thank you!
Thank u very much sir , u explained well
thanks man this will help me in price theory
Thanks a lot man
Masterpiece
Can it be used for other functions, like quasi-linear functions, or just COBB-DOUGLAS ?
No, I tried to make it clear that this shortcut only works for Cobb-Douglas- watch the video to see why. Every other kind of function is going to have very different looking derivatives, and MU, and thus MRS. However, there are some different ways (monotonic transformations) to transform a Cobb-Douglas that still represent Cobb-Douglas preferences. One example is to take the log of U: U=a*ln(x) + b*ln(y): The MRS will still be ay/bx.
does it work all the time sometimes for me it is opposite like a=0.5 b=0.5 i get mrs l/k when it shuld be k/l
If you want the slope with L on the x axis, then treat L like you would x. If Q=L^.5*K^.5, the MRTS=.5K/.5L=K/L.
@@BurkeyAcademy mrts is measured mpl/mpk so i guess that was why i got it wrong as mrs is measured using this method
Yeah, I know, I misspoke. :) You decide whether it makes you less painless, or not unpainfuller... or ... or something.
THANK YOU
Thank you SO MUCH
Legend!
Okay thanks a bunch! So for example the question is Q=f(L,K)=5KL^(1/4) I can use the rules in the video and assume that the MRTS = 1/4K / L or K/4L, and I can disregard the 5 because it cancels out?
MRTS(L for K) would be as you say, yes.
I'm getting a different answer for the first example. I get MUx= 0.2y^0.4 x^-0.8 and MUy=0.4x^0.2 y^-0.6 and then MRS = 0.5yx^-1.Why is that different than the shortcut/easy way?
0.5y*x^-1 is exactly the same thing as 1/2(y/x) or y/2x. 0.5=1/2, x^-1=1/x. (1/2)*y*(1/x)=y/2x.
BurkeyAcademy Thanks so much! As you can probably tell, this kind of thing isn’t my strong suit. 😬 Thanks for the video and the quick response!
Thanks for the video.
Can I ask a simple question?
The last example you wanted us to solve is U=x^0.7*y^0.1, right?
Isn't a+b always equal to 1?
On my textbook, Cobb-Douglas production function is: QO=A(K^aL^(1-a))
109=A(30^.3*70^.7)
A equals to 2, right? Can you please explain to me what "A=2" means here? Why do we need to calculate this?
Thanks again
Great questions. Question 1: a+b does not have to be =1. However, for Cobb-Douglas utility functions you CAN force a+b to be = 1, and it can still represent all possibly Cobb-Douglas Utility functions. Let me make a video about that- I have been meaning to, and can explain it very well that way very quickly. I am going to do my best to make a video about it in the next few hours. Please remind me if you don't see one soon, OK? Question 2: Same thing... let me make a short video response to this to try to explain WHY someone might force you to do this. Typing a response would bee hard and confusing! I'll go get a cup of coffee and see if I can get started!
BurkeyAcademy Thanks alot.
Your not-ready-yet video made me hit the subscription button :)
Okay lets wait :)
These "quick" videos sure take a lot of time!!! Here is #1: ruclips.net/video/8qYWvtXaJO0/видео.html
Your second video is up. Cheers-
You.... Sound like Tony Stark :D
Are these answers monotonic or non monotonic
Thank uuuuu❤❤
Got it. Thank you.
So monotinicity transforms the cobb-douglas function to:
U= x1^a . x2^1-a
So wouldnt it be solved as:
(du/dx1)/(du/dx2)
,therefore;
-a/(1-a) . x2/x1 ?
Is this as simple as it gets?
Yes, that would be the MRS! And there isn't a way to meaningfully simplify that further.
@@BurkeyAcademy you're amazing love your work !!
how can i apply this on a utility function with a square root? Thank you!!!
Do you know what power a square root represents?
'if you learn this trick it will make things much much less painless'....I don't want that!!
Thank you !!
Thanks!
in my text book has MRS= -U1/U2. with the negative in front. whats the difference? I think it should be negative since the indifference curve is downward sloping.
Yes, technically the slope is negative if both x and y are goods, and the slope of the budget line is negative as well. So, when solving MRS=Px/Py, I just cancel the negatives. Also, while the slope is negative, the MRS is a quantity that can be thought of as an absolute value: How many y you are willing to trade for 1 more x.
thanks a lot
If the values of x and y are given say MRS at x,y = (2,3) We follow the same steps right?
Plug the values of x and y into the MRS equation to get the slope at that point.
Thanks for the help. but does this work for MRTS when there are integers in front of X and Y, for example, q=10F^1/3 * K^2/3 ? Doesn't seem to be working for me, unless I've missed something silly.
Yes it does! The integers cancel out, since when you take the partial derivatives the 10 will appear in the numerator and denominator. One thing to be careful of is where you put your Pk and Pf-- that may be messing you up.
WHoever you are i LOVE YOU
Love you too, bud.
in the end, how does .7y = 7y and .1x = x ?
I just multiplied the top and bottom of the fraction by 10. So if (.7y)/(.1x) is exactly the same thing as (7y)/(x).
This might be a stupid question but, how did the decimal numbers become whole numbers in the end results? o_o
4/2 = 2
&
0.4/0.2 = 4
Its the ratio.
What if you had a constant in front of the x? Does that go away?
+Garin Flohr Yes, it does- because when you take the derivative the constant will be in the numerator and denominator, and will cancel.
nice
do you have videos with gravelle-rees excercises solved?
No, this is the first time I have heard of that book. Solving all of the exercises for one certain book is not something that would be interesting to do. But, if there is a TYPE of problem you would like help understanding, let me know.!
Do you have an easy way to find optimal bundle using cobb douglas?
I have a lot of videos on that, here is one: ruclips.net/video/mT4rVt4Kk_Y/видео.html If you need something different, let me know!
why does the 7 at the end go next to the Y ?
The exponent on the X always goes with the Y.
does this work for mrts too?
good
vallla eyyw mikro sorumzun aynisini cozmusunz thx a lot
My teacher made it so complicated :/
you forgot that MRS is always = - ; so you missed the negative
Most economists, and most textbooks call MRS the absolute value (and similarly with the marginal rate of transformation). Similar to the price elasticity of demand, we are not interested in the sign, but the magnitude.
Yes, there are a few sources that insist on the (-) sign, but it isn't important as long as you are consistent.
Thank you!
nice